Problem: Solve for $x$ and $y$ using elimination. ${-2x-3y = -18}$ ${2x+5y = 26}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. $2y = 8$ $\dfrac{2y}{{2}} = \dfrac{8}{{2}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {-2x-3y = -18}\thinspace$ to find $x$ ${-2x - 3}{(4)}{= -18}$ $-2x-12 = -18$ $-2x-12{+12} = -18{+12}$ $-2x = -6$ $\dfrac{-2x}{{-2}} = \dfrac{-6}{{-2}}$ ${x = 3}$ You can also plug ${y = 4}$ into $\thinspace {2x+5y = 26}\thinspace$ and get the same answer for $x$ : ${2x + 5}{(4)}{= 26}$ ${x = 3}$